ENDOR O F 4-IRRADIATED Y-TYPE ZEOLITES
2087
(40/P) = /vl; - vpeakl in megahertz. I n the companion paper it is shown that the experimentally obtained ENDOR spectra cannot be simulated by the conventional solid-state model. It was, in fact, just this observation that led to the present development of an alternative relaxation model.
Acknowledgment. One of us (J. C. V.) thankfully acknowledges a grant from NATO which made it possible for him to perform this work at Varian Associates in Palo Alto, Calif. We also wish to thank Professor Jack H. Freed for many helpful discussions and suggestions.
PROTON
Proton ENDOR of 7-Irradiated Y-Type Zeolites by Jacques C. Vedrine,’ James S. Hyde, and Daniel S. Leniart* V a r i a n Associates, Analytical Instrument Division, Palo Alto, California 9.4909 (Received M a y 80q1971) Publication costs assisted by V a r i a n Associates
This study is the initial application of electron-nuclear double resonance (ENDOR) to zeolites, and is, therefore, concerned to a large degree with methodology. Hydrogen atoms are trapped during y irradiation and the interactions between the atoms and surrounding protons are measured by ENDOR. Motion of the hydrogen atom modulates the dipolar interaction, causing nuclear relaxation of the protons which determines the nature of the ENDOR response. Well-resolved lines have been observed in H-Y-type zeolites. In this system it has been determined that the hydrogen atom is trapped in the center of the sodalite cage, and interactions with four different kinds of protons have been found. Sample treatment cycles found to be reversible using other methods have been found to be irreversible using ENDOR spectroscopy.
Introduction Many electron paramagnetic resonance (epr) experiments have been carried out by various workers on heterogeneous catalysts that have been subjected to the following treatment : careful degassing at some elevated “calcination” temperature, exposure at some other temperature to a gas or vapor, partial degassing at still another “activation” temperature, and subsequent y irradiation at 77°K.1-5 Hydrogen atoms are generally observed and occasionally other damage products. The hydrogen hyperfine couplings and g values may be shifted somewhat from the free atom the hydrogen atom yields and epr line widths vary rather considerably, and “spin flip” satellite lines of varying intensities are seen on either side of the hyperfine lines. From this intrinsic information content in the epr spectra, various inferences are made concerning the correlation with the Bronsted (H+) activity,za,8 the environment around the trapped hydrogen atoms, and the interaction of the gases with the catalysts. The present work represents an effort to apply, within this same general framework, the technique of electron-nuclear double resonance (ENDOR), with its intrinsically higher effective spectral resolution, to the investigation of hydrogen atom trapping sites of Y-type zeolites.
In the ENDOR experiments performed here we have adjusted the applied magnetic field to one of the hydrogen atom hyperfine lines and then slowly swept the incident nuclear radiofrequency through the region a few megahertz on either side of the free proton frequency, thus measuring the weak super-hyperfine interactions between the hydrogen atom and the surrounding protons. These are the interactions that give rise to the observed widths of the hydrogen atom epr hyperfine lines. To a very good approximation, the hydrogen atom spectra are isotropic. Thus all orientations contribute with equal intensity to the proton (1) Varian Associates Postdoctoral Fellow, 1970. (2) (a) P. H. Emmett, R. Livingston, H. Zeldes, and R. J. Kokes, J . Phys. Chem., 66, 921 (1962); (b) V. B.Kazansky, G. B. Pariisky, and V. V. Voevodsky, Discuss. Faraday Soc., No. 31, 203 (1961). (3) (a) J. C. Vedrine, G. Dalmai, and B. Imelik, J . Chim. Phys., 65, 1780 (1968); (b) J. C. Vedrine, G. Dalmai, and B. Imelik, “Proceedings of the Colloque Ampere,” Vol. XV, North-Holland Publishing Co., Amsterdam, 1969, p 304. (4) J. E. Wertz, J. W. Orton, and P. W. Auzins, Discuss. Faraday Soc., No. 31, 140 (1961). (5) J. H.Lunsford and J. P. Jayne, J. Chem. Phys., 44, 1487 (1966). (6) 8. N.Foner, E. L. Cochran, V. A. Bowers, and C. K. Jen, ibid., 32, 963 (1960). (7) F. J. Adrian, ibid., 32, 972 (1960). (8) A. Abou Kais, J. C. Vedrine, J. Massardier, G. Dalmai, and B. Imelik, C. R. Acad. Sci., Paris, Ser. C, 272, 883 (1971). The Journal of Physical Chemistry, Vol. 76, N o . 16,1978
20% EXDOR spectra. We refer to experiments of this type as powder EKDOR. In the companion to this paperj9we have developed :i theory of powder ENDOR relevant to the present work. Using this theory, it has been possible to obtain computer simulations of thc ENDOR spectra. The adjustable parameters in such a fit are (a) the number of spectroscopically inequivalent proton sites, (b) the radial distances between the proton sites and the hydrogen atom, (c) the relative populations of these sites, and (d) the amount of Fermi contact interactions with the protons. Thus, quite a lot of structural information can be obtained in those cases where well-resolved EXDOR spectra are observed with a good signal-tonoise ratio. In other circumstances, the interpretation is more qualitative, but often it is possible to reach meaningful conclusions particularly by comparison of the spectra from a series of samples treated in various ways. Additional ENDOR experiments on unordered solids are given in ref 10-12, and a general review of the ENDOR method in ref 13. The basic zeolite building block is the elementary tetrahedron of A104 or SiO,. There are four crystallographically inequivalent oxygen atoms, labeled 01, 0 2 , 0 3 , and 04, bonded to each Si,Al atom. In Y-type zeolites considered here there are 2.4 Si for each Al. Only one A1 can be bonded to each oxygen. That is, the structure A1-0-A1 does not exist. I n the vicinity of each A1 there is a cation or molecule that can neutralize the A1 minus charge. These tetrahedra are arranged to form cuboctahedra, also called sodalite cages or 0 cages. Each sodalite has eight hexagonal faces and six square faces. Roughly each sodalite contains a spherical cavity 6.6 in free diameter with 2.2 8 free diameter access through the hexagonal faces. Each sodalite is joined at four of the hexagonal faces to four other sodalites in tetrahedral symmetry. These junctions between two sodalite cages are formed by parallel hexagonal faces creating small cages known as hexagonal prisms. I n Figure 1, which is modeled after a figure by Smith,14 one can see a sodalite cage and three of the four hexagonal prisms associated with it. Each intersection in this figure is a tetrahedral site occupied either by A1 or Si. Rlidway between each intersection an oxygen is located. The Si-0-Si bonds form an angle of about 143”. The resulting 0 locations on one tetrahedral site are indicated in the figure. We have imagined that a hydroxyl proton could be on any one of the four oxygens and have indicated the positions of these protons in the figure. There can, of course, be only one such hydroxyl proton on a particular Al. The assembly of sodalites forms large supercages (also called CY cages). A supercage is formed by four hexagonal faces from four sodalites, six square faces from six other sodalites, 12 square faces from hexagonal prisms, and four large apertures which lead to other supercages. The supercages are roughly spherical with a diameter The Journal of Physical Chemistry, VoZ. 76, No. 16,1972
J. C. VEDRINE,J. S. HYDE,AND D. S. LENIART
Figure 1. The sodalite cage with three of the four attached hexagonal prisms shown. One A1 tetrahedral site is illustrated in detail and hydroxyl protons are imagined to be on each of the four adjacent oxygens.
of 13 A, and the connecting apertures are nearly round with a free diameter of 8 A. On a per-unit-cell basis there are eight supercages, eight sodalite cages, and 16 hexagonal prisms. The unit cell is 24.7 8 on a side. Helpful drawings have been given by BreckI5 and Meier and Olson.lo All sample preparations in the present work began with ammonium zeolite (NH4-Y type) that had been exposed to air and contained water and various other adsorbed gases. Upon heating this material under vacuum at 150°, substantially all of the extraneous gases, much of the water, and a small amount of ammonia are evolved. A maximum yield of hydrogen atoms is observed after y irradiation from samples heated at this temperature.8 It seems likely that the residual physically adsorbed water inhibits the formation of hydrogen atoms, and that these atoms come from the YH4+base exchange cations. I n the following it often will be convenient to refer to this particular (9) D. S. Leniart, J. S. Hyde, and J. C. Vedrine, J . Phys. Chem., 76, 2079 (1972).
(10) J. S. Hyde, G. H. Rist, and L. E. G. Eriksson, ibid., 72, 4269 (1968). (11) G. H. Rist and J. S. Hyde, J . Chem. Phys., 52, 4633 (1970). (12) L. E. G. Eriksson, J. S. Hyde, and A . Ehrenberg, Biochim. Bwphys. Acta, 192, 211 (1969). (13) J. S. Hyde in “Magnetic Resonance in Biological Systems,” A . Ehrenberg, B. G. Malmstrom, and T. Vaangard, Ed., Pergamon Press, Oxford, 1967, p 81. (14) J. V. Smith, Proceedings of the 2nd International Conference on Molecular Sieve Zeolites, Worcester, Mass., Sept 8-11, 1970, p 401. (15) D. W. Breck, J . Chem. Educ., 41, 678 (1964). (16) W. M . Meier and D. H. Olson, Advan. Chem. Ser., No. 102, 386 (1970).
PROTON ENDOR
OF
?-IRRADIATED Y-TYPE ZEOLITES
sample preparation as type I, and to use the same type I label for the resulting epr and ENDOR spectra and for the hydrogen atom sites giving rise to these spectra. When Y-type zeolites containing NH4+ are heated to 400” under vacuum, NHs is evolved; substantially no NH4+ remains. The protons that are formed on release of NH, cannot screen the negative charge on the alumina tetrahedra in the same way as do the much larger NH4+ or Na+ cations. Uytterhoeven, el a1.,17 suggested that the protons react with the lattice oxygen to form OH groups that were not present in the parent material. They give rise to two strong infrared bands a t 3550 and 3650 em-l. The intensity of these acid NH,+
H
I
OH bands is modified by introductions of basic compounds such as NH8, pyridine, piperidine, propylene, etc. Olson and Dempsey’* review the infrared literature on H-Y-type zeolites, emphasizing the uncertainties and disagreement in the literature in the assignment of these OH bonds to particular oxygens. They argue on the basis of rather indirect X-ray evidence that the 3550-em-’ band arises from OH groups in the hexagonal prisms on 0 3 oxygens. These OH groups are relatively inaccessible. The 3650-cm-l band has been associated with more accessible OH groups at the 01 axygens. These are the bridging oxygens between the faces of the hexagonal prisms and they extend into the supercages (see Figure 1). Wardl9 has systematically reviewed the literature on structural hydroxyl groups. A second maximum in hydrogen atom yield upon y irradiation is observed as a function of activation temperature at 400°.8 The hydrogen atoms almost certainly arise from a rupture of acidic OH bonds. We use the notation “type 11” to refer to this sample preparation and to the resulting sites and spectra. One of the objects in the present work was t o obtain structural information on the hydroxyl groups and to compare it with X-ray and infrared studies. The hydrogen atom is viewed as a “spin-label” and useful structural information would depend on the existence of a small number of hydrogen atom trapping sites, preferably one, in known locations, and not associated with structural defects or impurities. It will be argued later in this paper that the hydrogen atoms are trapped in unique sites in the geometrical centers of the sodalite cages and that the geometry of OH groups can indeed be studied with the ENDOR method. Upon calcination at 550” the OH groups are removed, there being almost no hydrogen left in the material, and an irreversible change in crystal structure occurs.
Experimental Procedures Sample Preparation. Ammonium zeolite was pre-
2089 pared from Linde sodium Y-type zeolite by base exchange at room temperature with an aqueous solution of ammonium chloride. Numerous exchanges resulted in a degree of exchange of 90% as determined by chemical analysis. Some experiments also were carried out with a 98yo exchanged NH4-Y zeolite kindly provided by Professor MI.Boudart. Sample material from the two sources resulted in identical ENDOR spectra. These samples were evacuated on a conventional vacuum system for 2 or 3 hr at room temperature before slowly increasing the temperature at the approximate rate of 60”/hr. All of the samples were maintained at the desired temperature overnight under a vacuum of less than lod4 Torr. For better degassing, the 8-mm sample tubes were set horizontally such that the powder layer thickness was less than 2 mm.*O This sample preparation was sufficient for our prototype investigation of type I and type I1 systems. Subsequently, other samples were prepared by introducing various vapors at room temperature into the vacuum system-either saturating vapor pressure for liquids or about 100 Torr for gases. We used propylene, methane, and ammonia (all Matheson, CP), pyridine (Aldrich Chemical Co.), DzO (Diaprep, Inc., 99.8%), and distilled water. The liquids were initially degassed by the freeze-pump-thaw technique. An additional step was employed for pyridine of drying over activated molecular sieves before distilling to a second flask for degassing. The duration of the vapor contact was 3-4 hr. I n some cases samples were subsequently evacuated at a second activation temperature for a t least 6 hr. We use a notation 400-NH3-155, for example, to describe a sample, where the first number gives the first activation temperature, the center entry is the vapor, and the final number is the second activation temperature. Irradiation was carried out with the sample in liquid nitrogen using a y-ray source of 0.8 n/lrad/hr for 15 hr (dose about 12 Mrads) at Raychem Co. in Menlo Park, Calif. After irradiation, the defects in the quartz sample tube were removed by tilting the sample tube so that the powder went to the other end of the tube, maintaining that end in liquid nitrogen and annealing the defects with a torch. Equipment and Technique. The spectra have been recorded using an E-9 Varian epr spectrometer equipped with an E-700 EXDOR system. This commercial apparatus is described in principle in ref 21. Experiments at 90°K were performed with a nitrogen flow (17) J. B. Uytterhoeven, L. G. Christner, and W. K. Hall, J . Phys. Chem., 69, 2117 (1965). (18) D. H. Olson and E. Dempsey, J . Catal., 13, 221 (1969). (19) J. W. Ward, Proceedings of the 2nd International Conference
on AMolecularSieve Zeolites, Worcester, Mass., Sept 8-1 1, 1970, p 682.
(20) G. T. Kerr, J . Catal., 15, 200 (1969). (21) J. s. Hyde, J. Chem. Phys., 43,1806 (1965) The Jozkrnal of Physical Chemistry, Vol. 76, X o . 16,1972
2090
J. C. VEDRINE,J. S. HYDE,AND D. S. LENIART
system, and experiments between 10 and 30°K with a liquid helium boil-off system described in ref 22. Careful measurements of microwave frequencies and magnetic fields were made to determine hyperfine splittings and g values with high precision. The techniques were similar in principle to those described by Segal, Kaplan, and FraenkeLZ3 Accuracies were *0.1 G and were limited by the epr line width and signal-tonoise ratio.
Epr Results and Discussion Hyperfine Splittings and g Values. When ammonium zeolite is treated according to procedure I, i.e., simply activating at 150" and irradiating at 77"K, a hydrogen atom doublet is obtained with a hyperfine splitting of 499.5 0.2 G. The line width is 3.15 G and the g value is 2.0023 0.0001, where a second-order correction has been introduced. When the material is treated according to procedure 11, i e . , activating at 400" and irradiating, a hydrogen atom doublet is obtained with a 0.2 G, line width of 1.25 G, and a splitting of 501.7 g value of 2.0023 f 0.0001. These hyperfine splittings can be compared with the value of 506.7 G for free protons. No line shape asymmetry could be detected, as would be expected if the hydrogen atom hyperfine interaction or g tensor were anisotropic. Line widths and shapes remained unchanged when the samples were investigated using a microwave frequency of 35 G H Z . ~ I n these systems the trapped H atom is almost free; the magnitude of the g value and hyperfine splittings are attributed to the isolated radical while small changes in these parameters are due to the interaction between the trapped radical and its environment. Adrianz4has calculated the shifts found for hydrogen atoms trapped in rare gas matrices. We can attempt to use his results by assuming that the fully coordinated Si-0 units may be simulated by argon atoms. Assuming a nonpolar matrix, Adrian considered the effects of both van der Waals forces and Pauli exclusion forces on trapped hydrogen atoms. The effect of the former is dominant at large distances and tends to expand the H atom wave function resulting in a reduction of the hyperfine splitting. The latter interaction dominates at close distances and contracts the wave function resulting in an increase of the hyperfine splitting. A plot of hyperfine shift us. radial distance thus goes from a positive value to a negative value and then asymptotically to zero. The Pauli or exchange interaction also leads to a negative shift in the g value. Much of the succeeding analysis will focus on H-Y zeolites-that is, on material prepared according to procedure I1 where the trapped hydrogen atom interacts with structural hydroxyl groups. Our epr data show a change of -0.98 ~.t0.04% in the hyperfine splitting for this sample. The most probable hydrogen atom trapping site consistent with Adrian's theory is the
*
*
The Journal of Physical ChemistrLl:, Vol. 76, No. 15, 1972
geometrical center of the sodalite cage. The walls of this cage consist of 24 Si(A1) atoms at a distance of 5.0 A, 12 0 atoms (03) at a distance of 4.3 A, and 12 0 atoms (02) at a distance of 4.5 A. Assuming that this wall can be equated to 30 argon atoms at an average distance of about 4.6 A results in good agreement between theory and experiment for the hyperfine interaction. Moreover, the predicted g shift is negligible, also in nearly perfect agreement with experiment. We have considered the center of the hexagonal prism as a possible trapping site. However, fairly large positive hyperfine shifts and large negative g shifts are predicted, in disagreement with experiment. Hydrogen Atom Yields. Returning to a description of other aspects of the epr behavior, the yield of H atoms is about the same for both type I and type I1 samples and is estimated to be about 10ls atoms/g. For type I1 samples, there are about loz1 OH groups and 0.1% are converted into hydrogen atoms. The yields increase linearly with dose up to about 5.2 Mrads and saturate at higher doses. Microwave Power Saturation. Progressive saturation experiments have been carried out on both type I and type I1 samples at 80 and 10°K. (H atoms disappear above 90°K.) The saturation appears homogeneous, consistent with Bloch equations. We consider this result surprising; we expected to observe saturation behavior characteristic of inhomogeneously broadened hyperfine lines.25~26 Saturation occurs at an incident power of 0.8 mW for type I1 samples and 1.6 mW for type I. These are the incident powers where the saturation parameter is Most remarkably, there was no observed temperature dependence of the powers at which saturation occurs. These saturation results are adequate for the present purposes: vix. optimizing the ENDOR signal-to-noise ratios; they are, however, sufficiently unusual that a more serious study probably using pulse methods would seem to be appropriate. Satellite Lines, On either side of each hyperfine line spaced an amount approximately equal to the nuclear Zeeman interaction, intense satellite lines have been observed. The satellites arise from induced transitions involving a change of both electron and nuclear magnetic quantum These "forbidden" transitions are observed because of a mixing of nuclear states, with mixing coefficients given by the ratio of the electron-nuclear dipolar interaction to the nuclear Zeeman interaction. These two interactions determine both the position and the intensity of the contribution from each (22) U. Ranon and J. S. Hyde, Phys. Rel;., 141, 259 (1966). (23) B. G. Segal, M .Kaplan, and G. K. Fraenkel, J . Chem. Phys., 43, 4191 (1965). (24) F. J. Adrian, ibid., 32, 972 (1960). (25) A. M . Portis, Phys. Eel;., 91, 1071 (1953). (26) J. S. Hyde, ibid., 119, 1492 (1960). (27) G. T. Trammell, H. Zeldes, and R. Livingston, ibid., 110, 630 (1958).
PROTON ENDOR
OF
209 1
7-IRRADIATED Y-TYPEZEOLITES
nearby proton of each crystallite, and the actual satellite lines would be constructed of a summation over all crystallite orientations and over all protons. There is a definite relationship between these satellite lines and the powder ENDOR spectra under consideration here. The characteristics of each are determined by the same interactions: nuclear Zeeman and electron-nuclear dipolar. If satellite lines are seen in the epr spectrum, one can expect successful ENDOR; if they are absent, ENDOR between the electron and matrix protons has generally been impossible to detect. I n ENDOR the two interactions determine the position of the contribution from each proton of each crystallite, and the dipolar interaction determines the intensity of the contribution inasmuch as it determines the nuclear relaxation probability. Indeed, it appears generally true that the intensities of ENDOR signals and of the epr satellites are proportional to each other. I n a rigid system, the ratio of the intensities of satellite line to central line has been given by Trammell, et al. (ref 27, eq 25)
le"
1 3 '
14
'
13
I4
' I5MHz
Figure 2. ENDOR spectra of NHa-Y zeolite: I, activated at 150'; 11, activated at 400'; A, observed at E o K ; B, observed a t 80°K. The arrows indicate the free proton frequency.
tion content mas substantially lower than has been achieved in the present work using EYDOR and interpretation was difficult. This expression is for a single electron interacting with a single proton and angular dependences have been dropped. Here He is the magnetic field at the proton from the electron. At 1 8, this field is 19 kG. These are induced transition probabilities; there is no consideration of relaxation phenomena. Stationary ENDOR signals are proportional to the nuclear longitudinal relaxation probability. If the fluctuating dipolar field from the relaxing electron relaxes the proton (ref 28, p 380), it can be shown that
which has the same form as eq 1. This is a specific situation where satellite and ENDOR signals are proportional to each other. I n the present work (see also the companion paper, ref 9), it has been determined that motion of the hydrogen atom plays an important role in determining the nature of the relaxation of nearby protons, and attention has been focused particularly on radial motion. It is clear that such motion also will affect that satellite epr lines; eq 1 will no longer be valid since the motion mill give rise to a time dependence of the mixing coefficients. This would appear to be a useful further calculation, perhaps modeled after Shimizu's work on the effects of torsional motion on satellite lines.29 The intensity and shape of satellite lines has been used by Vedrine as a probe of the environment of the H atom in irradiated zeolites and aluminum hydroxides.30 Differences were observed between samples treated in various ways) but the resolution or informa-
ENDOR Results on Type I and Type I1 Samples The ENDOR spectra for these samples at 15 and 80°K are shown in Figure 2 . I n Table I we have tabulated the positions of the peaks and have also attempted to give internally consistent relative H-atom yields and internally consistent ESDOR intensities for all samples studied here. Type I spectra show peaks at h0.14 R4Hz and shoulders at k0.30 MHz. Type I1 spectra show these same features, and in addition, well-defined peaks are seen at *0.56 and 3=0.72 MHz. These latter peaks show a marked temperature dependence. The dependence is reversible; there is no partial bleaching at the higher temperature. The EWDOR intensity of these strongly coupled lines relative to the center line is also dependent on the level of saturating microwave power. Looking back at Figure 2 , IA, one can imagine that these welldefined peaks correspond approximately to the weak pedestal observed there and that the apparent decrease of the pedestal in Figure 2 , I B is consistent with the decrease observed in Figure 2, IIB. We conclude tentatively that the trapping sites in type I and type I1 samples are similar and that hydrogens, one from each NHI+, in type I samples are approximately in the same locations as the hydroxyl protons of type I1 samples. The other NH4+ protons may be in less well-defined locations, causing some loss of resolution. (28) A. Abragam, "The Principles of Nuclear Magnetism," Oxford University Press, Oxford, 1961. (29) H.Shimiz;", J . them. P ~ U S . , 42,3603 (1965). (30) J. c. Vedrine, t o be published.
The Journal of Physical Chemistry, Vol. 76, N o . 16,1978
J. C. VEDRINE,J. S.HYDE,AND D. S. LENIART
2092 Table I : Summary of Epr and ENDOR Results
Matrix ENDOR intensity, arb. units
H-atom yield, arb. units
Couplinga from ENDOR, MHz
3.15 1.25 2.75 ( H ) 2.3 (D) 1.25 (H) 1 . 0 (D) 1.6 1.25 1.25 1.25 3.1
1.0 0.75 0.4 0.3 0.06 0.2 0.4 0.1 0.75
1.3
0.60, 0.28 1.45, 1.12, 0.30, 0.15 No resolved lines No resolved lines No ENDOR No ENDOR No resolved lines No ENDOR 1.00, 0.30 1.10, 0.35
400-NHa-155
1.3
2.6
1.00, 0.25
1.2
450-NHa-420 400-pyr-150 400-pyr-200 375-pyr-375 380-CaHe-(n0 degassing) 420-CaHe-310 650-CaHs-(n0 degassing) 450-CHh-(no degassing)
3.0 1.25 2.6 1.25 1.6 1.25 1.25 1.7 1.25
0.35 0.01 0.01
1.04, 0.35, 0.15 No ENDOR No ENDOR 1.15 1.04 0.95, 0.20 No ENDOR 1.00, 0.22
2.1
Epr line
Sequence
150 375 175-DzO-150 400-DzO-150 450-H20-150 400-H20-380 380-NHa-(no degassing) 335-NHa-145
width, G
The information content in type I spectra is not high enough to justify a more detailed analysis, but the good spectra from type I1 samples do justify more elaborate interpretation. I n the next section we apply the theory of powder ENDOR developed in the companion paperg to the present situation and demonstrate that it is capable of explaining these type I1 spectra.
Computer Simulation of ENDOR Spectra I n t r o d u c t i o n . The powder ENDOR line shape attributed to a single proton is determined by the Hamiltonian and by the specific type of nuclear relaxation that the proton undergoes. The spectrum is described by the shape function
X sin OdO (3)
where W,(O,ri) is the nuclear relaxation probability, ri is the radial vector between the hydrogen atom and the proton, 0 is the angle between r i and the applied magnetic field, and the remaining notation is given in the companion paperag Several models have been tested, evaluating eq 3 and comparing computer simulated spectra with actual ENDOR spectra. Each nuclear spin packet was assumed to have an intrinsic line width Tz,-l of 50 kHz in all calculations. The first model tested was to drop the explicit angular dependence of W,, varying the relative magnitudes of XDand XFCin an effort to achieve a best fit. I n nmr of dilute parama.gnetic solids,31it iS Customary The Journal of Physical Chemistry, Vol. 76, No. 16, 1976
0.4 1.5 0.4 0.07
0.5
1.0 1.0 1.7 1.9
0.8 5.0
0.8
2.0 10.0 17.0 20.0
to drop the angular dependence of nuclear relaxation caused by the electron, at least outside of a certain critical radius, because of nuclear spin diffusion. If XD >> XFC, the calculation amounts to fitting the experimental ENDOR spectrum by a sum of several Pake The outer peaks could be described fairly well by the pole arising from crystallites oriented such that 0 = 90" (Le,, (3 cos2 0 - 1) = -l), but the shoulders at 0 = 0 (;.e., (3 cos2 0 - 1) = 2) were not present experimentally. In addition, the valleys a t Y, 0.325 MHz (see Figure 1, IIA) were not well reproduced. It was possible to overcome some of these problems if it was assumed that XFC >> Xn. This circumstance seemed physically improbable, since it implies that t i e protons are quite far from the hydrogen atom (-7-8 A) but that the hydrogen atom interacts sufficiently strongly with the lattice to transfer considerable spin density to the proton through several chemical bonds. Moreover, we have been unable in a detailed way to justify the dropping of the angular dependence because of nuclear spin diffusion. A second model that has commonly been used t o describe nuclear relaxation in solids containing paramagnetic impurities is modulation of the dipolar interaction via the relaxing electron.2* This mechanism was used to describe the matrix ENDOR line that has been observed in various powder spectra;1° however, in the zeolite system it appears to be quite inappropriate. The main reason for disregarding it is that the sin2 0 . cosz 0 dependence of W , leads to a buildup of ENDOR
*
(31) w. E. Blumberg, Phys. R ~ . 119, , 79 (1960). (32) G. E. Pake, J. Chem. Phys., 16, 327 (1948).
PROTON ENDOR
OF
2093
?-IRRADIATED Y-TYPE ZEOLITES
intensity at the free proton frequency. Sin2B cos26 is a maximum a t 45", which is close to the magic angle of 54.7" where the dipolar interaction is zero. Again, if one assumes that XFC>> XD,the ENDOR spectra can be simulated. A small XDis required to get sufficiently narrow ENDOR lines and ai must be about 0.700 MHz. This set of circumstances is subject to the same criticism as the first trial model. The failure of these models has led to a consideration of the possible effects on proton relaxation of hydrogen atom motion modulating the electron-nuclear dipolar interaction. This model is discussed in detail in the companion papere and is outlined here. Effects of Motion of the Trapped Atom. The epr data and, as we shall see, the ENDOE spectra indicate that the hydrogen atom is trapped in the sodalite cage. The nuclei of the atoms formin$ this cage lie on a spherical shell approximately 9.4 A in diameter, and the free diameter of the cage is 6.6 A. The entrances to the cage have a free diameter of about 2.2 8, about the same as a hydrogen atom; below about 80°K the atom is trapped and above that temperature it escapes. There is no doubt that the atom will move in this cage, but a detailed description of the motion is of course difficult to make. If we allow the walls of the sodalite cage to be of infinite potential, it is possible to obtain an approximate estimate of the vibration frequency. One assumes Maxwell-Boltzmann statistics, attributing kT/2 of energy to each degree of freedom. At 20°K this frequency is in the high microwave range of 10l2 Ha. If one constrains the atom to the 6.6 8 diameter cage and considers the effect of motion on the dipolar interaction with hydroxyl protons, it is apparent that the magnitude of any angular fluctuations resulting from this motion is extremely limited and has very little effect on the nuclear relaxation. On the other hand, the magnitude of the fluctuations of ri can be quite large and have a profound effect on the dipolar interaction with the hydroxyl protons. I n ref 9, the effect of this radial motion on Wn was analyzed. The Hamiltonian itself (the exponential part of eq 3) is affected by this rapid motion only inasmuch as r i is replaced by pi. A jump model between two states was assumed. The dipolar interaction was written in a tensorial representation, and the five components were treated individually. A composite ENDOR spectrum was then simulated by adding them together-that is, by adding five integrals of the form of eq 3 for each proton. The sin2 B cos2 B pseudosecular Wfl terms cause a rather broad weak line at the free proton frequency. The total ENDOR line shape is quite insensitive to these terms. The (3 cos2 6 - 112 nonsecular ~0 term is peaked and the associated line widths are rather narrow. However, the sin4 @ nonsecular W*' terms are also sharply peaked and about an order
of magnitude greater than the Woterm. I n our simulations all terms have been included, but the W*2 terms make the dominant contribution to the experimentally observed line shape with two peaks at Y. f (yeail2 ai) (or -ai if the spin density is of opposite sign). This type of analysis is applicable when the motion of the trapped H atom is described by a jump
